PSI - Issue 64

Francesco Focacci et al. / Procedia Structural Integrity 64 (2024) 1557–1564 Author name / Structural Integrity Procedia 00 (2019) 000–000

1561

5

solution, i.e., the slip ( ) λ s z , axial force ( ) λ N z , and rotation ( ) λ ϕ z profiles associated with a load multiplier λ are determined, the deflection (transversal displacement of the midspan cross-section) can be computed by integration of the rotation profile. The presented model can be used to determine the load response of a strengthened beam, i.e., the relation between the load multiplier λ and the displacement v of the midspan cross-section.

N ( z )

D

a

b

q ( z ) = λ q 0 ( z )

AB C

τ ( s )

z

z f

z = 0

H

L f L t

s

v

λ q

λ q

Point A

Point C

s ( z )

s ( z )

s Μ

s Ε

z

z

-s Ε

-s Μ

N ( z )

N 0 ( s M , λ)

N ( z )

c

e

z

z

ϕ( z )

ϕ( z )

∆ϕ 0

z

z

ε c ( z )

ε c ( z )

ε t

ε t

z

z

z f

z f

-z f

-z f

z c 2 -z c 2

z c 3

λ q

λ q

Point B

Point D

s ( z )

s ( z )

s Μ

s Μ

z

z

-s Μ N ( z )

-s Μ

N ( z )

N 0 ( s M , λ)

N 0 ( s M , λ)

d

f

z

z

ϕ( z )

ϕ( z )

∆ϕ 0

∆ϕ 0

z

z

ε c ( z )

ε c ( z )

ε t

z

z

z cj

z cn

z f

z f

-z f

-z f

z c 2 -z c 2

z c 2 -z c 2

Fig. 3. (a) Simply supported strengthened concrete beam; (b) load response; (c) solution for the uncracked beam; (d) solution for the beam with one crack; (d) solution for the beam with three cracks; (f) solution for the beam with n cracks.

The profiles of the slip, axial force, and rotation corresponding to different load levels, the evolution of the cracking process, and the failure mode may also be evaluated. Due to the symmetry of the beam, only its right half ( 0≤ z ≤ L t /2) is considered when describing the solution strategy adopted.